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Table 2 Standardization of the risk ratio

From: On the collapsibility of measures of effect in the counterfactual causal framework

  Men Women
Exposed cases (n) 100 200
Exposed non-cases (n) 400 300
Unexposed cases (n) 400 300
Unexposed non-cases (n) 100 200
Risk Ratio 0.25 0.6667
\(\hbox {Pr}(V=v)\) 0.5 0.5
\(\hbox {P}(Y=1 \vert A=0, V=v)\) 0.8 0.6
Weight 0.4 0.3
  1. Table shows a simple toy example of 2000 subjects, of whom 1000 are exposed to a drug. Here, the covariate V denotes gender, and we assume no unmeasured confounders. The marginal causal risk ratio can be calculated as \(\frac{0.25 \times 0.4 + 0.6667 \times 0.3}{0.4+0.3}=0.428\). Note that the weights are easy to obtain: \(\hbox {Pr}(V=v)\) is just the probability of belonging to the gender, and \(\hbox {P}(Y=1 \vert A=0, V=v)\) is the probability of the outcome among the unexposed in that gender